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Please use this identifier to cite or link to this item: http://ntour.ntou.edu.tw:8080/ir/handle/987654321/24577

Title: Null-field approach for Laplace problems with circular boundaries using degenerate kernels
Authors: Jeng-Tzong Chen;Wen-Cheng Shen
Contributors: NTOU:Department of Harbor and River Engineering
國立臺灣海洋大學:河海工程學系
Keywords: degenerate kernel;Fourier series;multiply-connected domain problem;null-field integral equation;semi-analytical approach
Date: 2009-01
Issue Date: 2011-10-20T08:12:51Z
Publisher: Numerical Methods for Partial Differential Equations
Abstract: abstract:In this article, a semi-analytical method for solving the Laplace problems with circular boundaries using the null-field integral equation is proposed. The main gain of using the degenerate kernels is to avoid calculating the principal values. To fully utilize the geometry of circular boundary, degenerate kernels for the fundamental solution and Fourier series for boundary densities are incorporated into the null-field integral equation. An adaptive observer system is considered to fully employ the property of degenerate kernels in the polar coordinates. A linear algebraic system is obtained without boundary discretization. By matching the boundary condition, the unknown coefficients can be determined. The present method can be seen as one kind of semianalytical approaches since error only attributes to the truncated Fourier series. For the eccentric case, vector decomposition technique for the normal and tangential directions is carefully considered in implementing the hypersingular equation in mathematical essence although we transform it to summability to divergent series. The five advantages, well-posed linear algebraic system, principal value free, elimination of boundary-layer effect, exponential convergence, and mesh free, are achieved. Several examples involving infinite, half-plane, and bounded domains with circular boundaries are given to demonstrate the validity of the proposed method.
Relation: 25(1), pp.63–86
URI: http://ntour.ntou.edu.tw/handle/987654321/24577
Appears in Collections:[河海工程學系] 期刊論文

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